In so-called temperate climates, where the ambient temperature and humidity can vary between wide limits, pipes carrying water are subjected to conditions at various times that can cause sweating, loss of heat if the water has been heated, and freezing of the water. This invention relates to the entire spectrum of such problems and in particular provides a pipe covering and heating system which is low in cost, easy to install, uses components that are readily available, and minimizes use of materials that are difficult to work with or are in critical supply. The system of the invention when installed on a waterpipe constantly inhibits sweating and minimizes loss of heat from hot water, and optionally provides heating means to prevent freezing of water in the pipe; in the latter function it makes maximum use of pipe heating devices in a manner which, as a practical matter, has not up to now been available to consumers.